Faceted reflector

ABSTRACT

The present invention provides a reflector, e.g. for a desk lamp, which is designed to provide an unusual predetermined pattern of illumination on a surface, for instance a pattern having non-concentric isolux curves around a point of strongest illumination, and which results in a more even distribution of light over the surface illuminated. The reflector is particularly designed for uniformly illuminating a predetermined area, even at a comparatively large distance from the vertical projection of the light source on the said area. For that purpose, the reflector is built in the form of a complex surface comprising a plurality of elementary reflecting surfaces each of which has a distinct shape. The elementary reflecting surfaces are linked to one another at their upper and lower edges through continuous surfaces portions and at their lateral edges through stepped surfaces portions called redans. The horizontal and vertical traces of the tangent planes to the various points of said individual elementary reflecting surfaces are so located respectively on horizontal planes containing said various points and on vertical planes containing both said points and a predetermined point of the source of radiation which cooperates with the reflector so as to provide, on a horizontal area to be illuminated, a plurality of images of the source, said images cooperating for giving a continuous predetermined level of illumination of the said area.

United States Patent Planchon 5] Oct. 24, 1972 [54] FACETED REFLECTORJean Planchon, 9, rue Chaptal, Paris 9eme, France [22] Filed: Sept. 2,1970 [21] Appl. No.: 68,951

Related US. Application Data [63] Continuation-in-part of Ser. No.695,522, Jan.

3, 1968, abandoned.

[72] Inventor:

[52] US. Cl. .240/41.36, 24.0/ 103 R [51] Int. Cl ..F2lv 7/09 [58] Fieldof Search ..240/103 R, 8.3, 41.36

[56] References Cited UNITED STATES PATENTS 1,535,985 4/ 1925 Clark..240/41.36 X 1,566,906 12/ 1925 Matisse et al ..240/41 .36

Primary Examiner-Jerry W. Myracle Attorney-Cushman, Darby & CushmanABSTRACT The present invention provides a reflector, e.g. for a desklamp, which is designed to provide an unusual The elementary reflectingsurfaces are linked to one another at their upper and lower edgesthrough continuous surfaces portions and at their lateral edges throughstepped surfaces portions called redans. The horizontal and verticaltraces of the tangent planes to the various points of said individualelementary reflecting surfaces are so located respectively on horizontalplanes containing said various points and on vertical planes containingboth said points and a predetermined point of the source of radiationwhich cooperates with the reflector so as to provide, on a horizontalarea to be illuminated, a plurality of images of the source, said imagescooperating for giving a continuous predetermined level of illuminationof the said area.

3 Claims, 27 Drawing Figures PATENTEDHBT24 I912 3 700882 sum 1 0F 7PATENTED I97? I 3.700 882 SHEET 2 0F 7 PATENTEDUEI 24 I972 SHEET 7 [IF 7FACETED REFLECTOR This application is a continuation-in-part of Ser. No.695,522 filed Jan. 3, 1968 and now abandoned.

BACKGROUND OF THE INVENTION The present invention relates to reflectorsfor reflecting light or heat. It will be more particularly disclosedhereinafter with reference to lighting devices, though it may be alsoapplied to other types of radiation.

Standard lighting devices comprise a light source, consisting either ofa bright or frosted bulb, or of a fluorescent tube, placed inside adiffusing reflector, the entire assembly providing for the lighting ofcertain area. In the special case of an individual lighting device, tobe placed, for example, on a desk or a table, the light source-diffusingreflector assembly provides for'the illumination of a work plane and thediffusing reflector, acting as a lampshade, provides in addition, forthe concealment of the bulb with respect to the eye of the user so asnot to dazzle him. The diffusing reflectors commonly used to obtain suchilluminating means, whether general or individual, have, for reasons ofconvenience of manufacture, simple geometrical forms such as a frustrum,a portion of a right cylinder with a circular elliptical, rectangular orparabolic base, a paraboloid, a portion of an ellipsoid or a formresulting from the association of two or more of the previouslymentioned simple geometrical forms.

The devices thus constructed have the disadvantage of not providing theillumination of the area to be illuminated in a manner which issystematically adapted to needs and, in particular, in the case of'individual lighting devices, of not producing an illumination allowingfor good vision. Certain known reflectors provide a concentration ofenergy in one or more preferential directions, but do not, in asystematic fashion, allow for the distribution of energy from the sourceon a predetermined area and, in accordance with a predetermined level ofillumination, which may consist, as a specific example of particularinterest, in an uniform illumination over the entire range of saidpredetermined area.

In the particular case of individual lighting devices, it is observed,with standard devices, that the isolux curves measurable on the workplane are generally concentric and that the illumination decreasesrapidly from the point benefiting form the strongest illumination, saidpoint being, most often, located vertically with respect to the lightsource. For example, with a 75 watt bulb placed approximately 30 cmabove the work plane and laid out along the axis of a reflector whoseopening is parallel to the work plane, the entire assembly giving anillumination of 2,600 Lux at a'central point located vertically withrespect to the bulb, an illumination of 1,000 Lux at a distance of 25 cmfrom the central point was noted, of 600 Lux at a distance of 33 cm fromthe central point and finally of 200 Lux-only at a distance of 52 cmfrom the central point. It follows that, if a work item 40 cm wide isplaced in the illuminated area so that its center is located at anillumination point of 400 Lux, one of its edges will be located at anillumination point of approximately 1,000 Lux and the other one of itsedges at an illumination point of the order of 100 Lux; one of thehalves of the work item will therefore have an average illumination ofthe order jection of the light source on the said area. For thatv of 700to 800 Lux while the other half of the work item will have an averageillumination of approximately 200 Lux, and when the user views any pointin the work item, one of his eyes will have in its visual field, asurface whose average illumination will be very much stronger than theaverage illumination of the surface located in the visual field of hisother eye, which leads to a different accommodation for each eye, thuscausing visual fatigue. Moreover, if an effort is made, by increasingthe power of the light source, to increase the illumination of that halfof the work item receiving the least illumination, an illumination sointense of the other half is liable to be obtained, that the latter,even weakly brilliant, will act as a mirror and create a dazzlingeffect, thus increasing visual fatigue still further. In order todiminish the intensity of this defect, a diffusing bowl is sometimesplaced beneath the bulb, but the effect of the latter, in fact, is tolevel out the illumination of the work plane by lowering itconsiderably, which leads to either insufficient illumination or toneedlessly high power consumption, and this subsequently limits usage ofindividual illuminating devices, taking into account high illuminationlevels generally considered necessary.

Similarly, certain reflectors provide for the concentration of lightenergy from the source in one or several preferential directions, but ifthe isolux curves are considered in the regions comprising and in thevicinity of said preferential directions, it is observed that, hereagain, the illumination decreases vary rapidly from the point at whichthis illumination is a maximum.

SUMMARY OF THE INVENTION The present invention provides a reflector, egfor a desk lamp, which is designed to provide an unusual predeterminedpattern of illumination on a surface, for instance a pattern havingnon-concentric isolux curves around a point of strongest illumination,and which results in a more even distribution of light over the surfaceilluminated. The reflector is particularly designed for uniformlyilluminating a predetermined area, even at a comparatively largedistance from the vertical propurpose, the reflector is built in theform of a complex surface comprising a plurality of elementaryreflecting surfaces each of which has a distinct shape.

The elementary reflecting surfaces are linked to one another at theirupper and lower edges through continuous surfaces portions and at theirlateral edges through stepped surfaces portions called redans. Thehorizontal and vertical traces of the tangent planes to the variouspoints of said individual elementary reflecting surfaces are so locatedrespectively on horizontal planes containing said various points and onvertical planes containing both said points and a predetermined point ofthe source of radiation which cooperates with the reflector so as toprovide, on a horizontal area to be illuminated, a plurality of imagesof the source, said images cooperating for giving a continuouspredetermined level of illumination of the said area.

In a preferred embodiment, the reflector has a top wall and a generallycylindrical sidewall divided into a front portion extending throughoutabout l0-l30, two opposing side portions each extending throughout about30-60 and a rear portion extending throughout about 130-l80. One portionof the top wall of the reflector is designed to reflect light generallyaxially toward the surface to be illuminated. Another portion of the topwall, near the front 'of the reflector, is angled to substantiallyprevent direct incidences of light thereon from the source.

The inventor has also devised and described herein a method fordetermining what orientation of the individual mirrors will result inproviding the overall pattern of illumination desiredThis methodcomprises the steps of selecting a plurality of points on a surfaceapproximating the final reflecting surface of the reflector, ofdetermining, for each of the said points, the horizontal intersection ofan infinitesimal reflecting surface located at said point on anhorizontal plane containing said point and the vertical intersection ofthe said infinitesimal reflecting surface with a vertical planecontaining both said point and a predetermined point the source ofradiation; of locating, at each of said points, a concave mirror tangentto the infinitesimal reflecting surface thus determined, and .of joiningthe said concave mirrors to one another through curved reflectingsurfaces adapted for providing, with the said concave mirrors, acontinuous and smooth reflecting surface.

Preferably, the determination of the horizontal and verticalintersection is respectively carried, for each of the infinitesimalreflecting surfaces, through a determination of the angle defined, onone hand, by the bisectrix of the angle between the line which joins thesaid predetermined point of the source to the selected point on thereflector and the line which joins the said selected point to apredetermined point on the work plane and, on the other hand, by theline which joins the said selected point to the middle point between theorthogonal projections,'on the said horizontral plane, of the saidpredetermined point of the source and of a further point located on theline which joins the said selected point to the said predetermined pointof the source, and through a determination of the angle defined, on onehand by the said bisectriX and, on the other hand, by the line whichjoins the said selected point on the reflector to the middle pointbetween the said predetermined point of the source and the orthogonalprojection of the said further point on the said vertical plane.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagrammatic view showinga plane mirror, an area to be illuminated, and the path of a light rayoriginating from a light source and, after reflection on the mirror,converging on the said area;

FIG. 2 illustrates a vectorial representation of the intensity ofradiation around a point on a perfectly diffusing surface;

FIG. 3 is a diagrammatic view showing the useful solid angle belowwhich, in practice, a point can see a light source consisting of afrosted bulb;.

FIG. 4 shows diagrammatically the form of the image of a frosted bulbproduced on a work plane through reflection, at a point on a planemirror, of rays emitted by said frosted bulb;

FIG. 5 illustrates diagrammatically the method of determination of theintersection of one of the elementary mirrors, which makes up areflector in accordance with the invention, with a ground plane passingthrough the central point of this elementary mirror;

FIG. 6 shows diagrammatically the method of determination of theintersection of such an elementary mirror with a vertical plane passingthrough the central point of this elementary mirror and through thelight source;

FIGS. 7a and 7b are diagrams illustrating the construction of areflector according to the method set forth in FIGS. 5 and 6, FIG. 7ashowing the horizontal projection of the traces of the reflectorsections by ground planes of various levels and FIG. 7b showing, broughtdown on a same plane, the traces of the reflector sections throughvertical planes passing through the center of the source and makingvarious angles with the plane of symmetry of the reflector;

FIG. 8 is a sectional view of a projector constructed in accordance withthe result of the method explained in connection with FIGS. 7a and 7b;

FIGS. 9a and 9b show diagrammatically the illumination area obtainedusing the reflector shown in FIG. 8;

FIGS. 9c, 9d and 9e are diagrammatic views illustrating a particularapplication of the method for reflector design to the embodiment ofFIGS. 7a-9b.

FIG. 10 shows another construction of a reflector built using the samemethod as above, which is also adapted for lateral illumination andcooperates with a frosted bulb;

FIGS. 1la-1 1b and 12a-12b show embodiments of a reflector according tothe invention, said reflector partially surrounding alight sourceconsisting of a bulb;

FIG. 13 shows, as a section, an arrangement of decorative glassware,part of which was molded so as to show a structure according to theinvention and thus act as a reflector;-

FIGS. 14a and 14b illustrate the manner according to which a fluorescenttube illuminates a given point;

FIGS. l5a-l5b and l6a-16b-16c show embodiments of a reflector accordingto the invention, said reflector providing for the distribution of lightenergy produced by a fluorescent tube.

DETAILS OF PRESENTLY PREFERRED EMBODIMENTS OF THE INVENTION OPTICAL ANDMATHEMATICAL CONSIDERATIONS In order that the basic concept of theinvention may be more readily understood, a theoretical analysis of theprocess of illumination of a plane area from a complex reflectingsurface will now be given. FIG. 1 shows a light source consisting offilament 1 of an incandescent lamp, a plane mirror 2 and a work plane 3to be illuminated.

If any point P on mirror 2 and perpendicular line PN at P to said mirroris considered and if any point S of filament l is considered, it isknown that light ray SP will be reflected at P along PR so that straightli ngs SP, PN andPR are in a same plane and that angles SPN and P areequal. It follows that point R is the image of point S on plane 3, givenby the infinitesimal element surrounding point P in plane mirror 2.Since mirror 2 is assumed to be perfectly reflecting, i.e.,non-diffusing, ray PR is the only reflected ray corresponding toincident ray SP. If, now, all the points of filament l emitting lightrays in all directions are considered, there is, for each of saidpoints, one and only one light ray reaching P and it is reflected alonga single direction, so that a well-defined image 4 of filament 1 will beobtained on plane 3 formed of a plurality of juxtaposed infinitesimalplane mirrors such as mirror 2. It will give on plane 3, an illuminatedarea obtained by placing side by side an infinite number of well-definedand controllable images from the source, and it follows that the lightintensity at each point of said illuminated area will be accuratelycontrollable.

FIG. 2 illustrates a well-known vectorial representation designed toshow the distribution of light in various directions around a point Q ofa nonreflecting and perfectly diffusing surface. According to thisrepresentation, if the value of l is assigned to the vector showing thelight intensity along the perpendicular line at Q to said surface; thelight intensity along any direction will be represented by a vectorwhose extremity is on a sphere of diameter 1 tangent at Q to saiddiffusing surface. It follows, in accordance with the well-knownrelationship in right triangles, that the light intensity emitted in a45 direction with respect to the perpendicular is only 0.707 times thatemitted along this perpendicular, that the light intensity emitted in a60 direction with respect to the perpendicular is only 0.5 times thatemitted along this perpendicular and that the intensity decreases veryrapidly as the angles increase beyond'60. This means, as shown in FIG.3, that it is possible in practice, when a frosted light source isviewed from a point P, to take into account only the points of thissource such that a straight line joining them to point P makes an anglebelow 60 with the perpendicular at the source surface to the point underconsideration. Under these conditions, it can be seen on FIG. 4 that theimage of a light source such as 5, consisting of a frosted bulb, andproduced on a work plane 6 be reflection at a point P from a planemirror 7 of various rays originating from various points of said bulb,will be a well-defined surface. If the bulb is spherical, the total sumof the rays originating from its different points and leading up to Pwill make up a cone having a right circular section with apex P, thetotal sum of the reflected rays will make up a cone of apex P and ofperfectly well-defined generatrices whose intersection with the workplane will be an ellipse. This ellipse will present a central area withstrong illumination corresponding to rays originating from points on thebulb emitting towards point P along a small angle with respect to theperpendicular to the surface of the bulb, said central area beingsurrounded by areas of decreasing illumination corresponding to pointsin the bulb emitting towards point P along progressively larger angles.

In accordance with the basic concept of this invention, a reflectoradapted for providing for a predetermined distribution of lightintensity from a source on a given area will consist of a large numberof small elementary mirrors placed side by side with differentorientations.

POSTULATE From the above considerations, it clearly results that, takinginto account the nature and the position of the light source, theintensity of illumination produced by each elementary mirror on saidarea and the respective orientations of the elementary mirrors maybedetermined so that the illuminated areas produced by them are placedside by side or are superimposed so as to provide the desiredpredetermined illumination on the total area to be illuminated.

' THE METHOD, IN GENERAL A practical method for effecting saiddetermination will consist in determining, at various points of the areato be illuminated, the form and dimensions of the imageof the sourceseen by reflection on various elementary mirrors located at pointschosen a priori on the surface of a reflector having the desireddimensions and in determining the inclinations required for saidelementary mirrors so that the images given by them of the source on thework plane will be suitably placed P of the reflector and striking workplane 8 at R.

FIG. 5 also shows plane 10 passing through point-P and parallel to plane8, which is therefore horizontal as well as vertical plane 11 containingpoints S and P; this plane makes an angle H with vertical plane 12 goingthrough point 8 and constitutes a reference plane; finally, a point Bwas marked on ray PR such that PB will be equal to the distance PS andpoints B and S were joined by a straight line. According to Descarteslaws, perpendicular PN at P, to the infinitesimal plane mirrorsurrounding this point and causing the reflection of the incident ray SPalong PR, is within the plane defined by the three points S,.P and R andis the median relative to apex P of isoceles triangle SPB; this medianintersects side SB at a point M. At points 5,, M, and B, on FIG. 5, canbe seen the orthogonal projections of points S, M and B on plane 10 andit is evident that point M, is the midpoint of segments 3,, S, i. e. PM,is the median relative to apex P of triangle S,PB,.

If the intersection of the infinitesimal plane mirror, surrounding pointP, with plane 10, is represented by a segment of a straight line 13, itis evident that said segment 13 is orthogonal to PM,. It follows, if itis possible to determine, through calculation, the direction of the halfstraight line PM, in plane 10, that the trace of this plane of theinfinitesimal plane mirror surrounding point P will be immediatelydeduced. Now, since the relative positions of points S, P and R aredefined, the distances PS and PR are known, aswell as angle H of thedihedron formed by vertical planes 11 and 12, angle SPS,, that is dwhich, by the way, is equal to the angle formed by segment SP with theground plane passing through S, angle S,,P,,R with S and P being termedthe orthogonal projections of S and P on plane 8, angle PR P and finallyangle S P R which is equal to angle I-I, increased or reduced, dependingon the case, by an angle B which defines the angular position of point Rwith respect to the vertical plane passing through P and which isparallel to plane 12. If angle PR P is termed r, which is equal to angleB P B,, it can be seen that the following relation exists at B, in righttriangle P B 8,:

v sr= ol o and the value of side P S, can be calculated at S, in righttriangle PS ,8 using the relation PS =PScosd FIG. 6 shows, at M, and E5,the orthogonal projections of points M and Bon plane 11, and, as for thecase in FIG. 5, it can be seen that the half straight line P M is themedian originating at P in triangle P B S. Now,

since side PS, in this triangle, is'known, it is possible to calculateside PB which, in triangle PB: B, is given by:

I P B =PBcosy orPB =PScos7 by terming angle R P R, as 7, point R, beingthe orthogonal projection of R on plane 11. Now it is possi-- ble todemonstrate that angle 7 can be calculated using the formula:

sine'y=cosrsin(H+D) 1 indeed, let 7 be angle P P R,,; considering P inright triangle P P, R the following relation can be written:

P R,,=PP,,tga 2) Furthermore, considering R in right triangle P,,R,R,the following relation can be written P,,R,,=P,,Rcos(H+D) 3) Finally,considering P, in right triangle PP R, the following relation can bewritten P,,R=PP,, cotgr These relations (2), (3) and (4) give tg'y=cos(H+D) cotgr 5 Now, in right triangle PR R, the following relation can bewritten R R=PRsiny 6 Similarly, at R inright triangle R,,P,,R, thefollowing relation can be written v R,,R=R,,P tg (H+ D) 7 Furthermore,at -P,, in right triangle R P P, the following relation can bewritten IP R =PP tga it (8) Finally, at P in right triangle PP R, the followingrelation can be written Equations(6),(7),(8) and(9)lead tosin'y=zg(H+D)tgasinr By replacing tg a by its value given in 5), one canwrite:

sin 'y tg (H+D) sin r cos (H+ D) cotg 'r *or'by replacing the tangentsand cotangents by their I sin 'y=cos rsin (H+ D) which is actuallyexpression 1 It is therefore possible, knowing the relative positions ofpoints S P and R, i.e. the values of angles r, H and D, tocalculate thevalue of P B, and carry it on half straight line P R, which may beconstructed geometrically knowing angle or using formula (5 It istherefore possible to determine the position of point M and subsequentlyhalf straight line P M It is therefore known to construct segment 14which is perpendicular at P to said half straight line P M said segmentbeing the intersection of plane 11 with the infinitesimal plane mirrorsurrounding point P, causing the reflection along ,PR of ray SP. Underthese conditions, given a point S in the source, a point R in the areato be illuminated and a point P on the surface of the reflector, it ispossible to determine the plane mirror which must be placed at P for raySP to be reflected along PR, this determination being made byconstructing straight line segments corresponding to the intersectionsof said mirror with the ground plane passing through point P and withthe vertical plane passing through points P and S. Furthermore, knowingthe angle at which point P sees filament 9, it is possible to calculatethe shape of the image of said filament on the area to be illuminatedand toevaluate its relative contribution to the illumination of the areato be illuminated.

HOW TO APPLY THE METHOD The general shape and size of the reflector isfirst decided upon. For instance, the general shape may be that of aninverted bowl (for an incandescent bulb) or that of an inverted trough(for a fluorescent light). The reflecting areas of the roughed-outreflecting surface are then divided into a plurality of individual sitesor points. Using the method, it is possible to determine the spatialorientations or positions required for infinitesimal plane mirrorsplaced at these points so that the images provided by them will bedistributed on the area to be illuminated so as to give a predeterminedlevel of illumination. The entire surface of the reflector can then beobtained by providing a complex reflecting surface set up by placingedge to edge plane mirrors constructed along the horizontal and verticaltraces detemiined as indicated above and joined to one another throughobtuse angles or through more or less emphasized bends, thus giving acontinuous illumination of the work plane due to the spread of theinfinite number of images produced by the infinite number ofinfinitesimal mirrors comprising each one of said plane mirrors. Inpractice, the size of the bends is decreased and the precision of thedistribution of illumination on the area to be illuminated is increasedby replacing such plane mirrors by concave mirrors tangent at eachpoint, such as P, to the plane mirror determined as in-' dicated above.The determination of the curvatures of said concave mirrors" is carriedout graphically or through calculation according to methods well-knownto those skilled in the art.

FIGS. 7a and 7b show the result of a determination conductedaccording'to this method. The result is expressed in the forrr'i ofcurvesrepresenting, in FIG. 7a, the intersection of the internal face ofa reflector built in accordance with the invention, with the groundplanes of different levels and, in FIG. 7b, the intersection of theinternal face of the reflector with the vertical planes passing throughthe center of the source and forming, with a vertical plane ofreference, which in this particular case, is the plane of symmetry ofthe projector, angles of increasing size, said intersections beingbrought down on said plane of symmetry. The curves of FIG. 7a are shownas a succession of curve segments determined according to the methoddescribed and linked to one another through step-shaped connectionscorresponding to bends between the corresponding surfaces. The curves inFIG. 7b are shown as continuous curves obtained by connecting togethercurve segments obtained according to the method described. FIG. 7a showsonly the curves relating to half of the projector, the second half beingobtained through symmetry with respect to axis AA. FIG. 7a shows traceof the intersection of the internal surface of the reflector with theground plane passing through center S of the source. This trace takesthe form of a succession of curve segments, connected to one anotherthrough curvilinear links, so that said curve 15 actually takes the formof a continuous concave curve except at point 16 which corresponds tothe junction of the front part and back part of the reflector, ofdifferent dimensions. This junction takes the form of a large bendpractically perpendicular to the parts of said curve 15 enclosing it.FIG. 7a also shows the intersections of the internal surface of thereflector with the ground planes located at different levels above andbelow the preceding plane, i.e. curve 17 corresponding to the level 8centimeters, curve 18 corresponding to the level 16 centimeters, curve19 corresponding to the level 8 centimeters and curve 20 correspondingto the level 19 cen timeters.

These curves show, at the level of bend 16 of curve 15, similar bends21, 22, 23 and 24. Furthermore, curves l7, l8, l9 and 20 take the formof a succession of curve segments which, instead of forming a connectedseries as in the case of curve 15, are linked to one another through aslight dent forming a step such as 25 or 26.

The curves in FIG. 7b take the form of a succession of curve segmentsforming a connected series with one another. Curve 27 corresponds to theintersection of the back part of the reflector with the vertical planepassing through the center of the source and forming a null angle withthe plane of symmetry. Furthermore, curve 27 ends up downwards as anoblique part 28 and a circle 29 corresponding to a rolled edge of theprojector whose purpose is to increase rigidity, and upwards as ahair-pin-shaped part corresponding to the upper edge of the reflectorconveniently shaped so as to provide sufficient rigidity to theassembly. Curve 31 corresponds to the intersection of the forward partof the reflector with a vertical plane passing through the center of thesource and forming an angle of 20 with the plane of symmetry of thereflector. The said curve is similar to curve 27. This is similarly truefor curves 32, 33, 34, 35 and 36 corresponding respectively to angles of65, 75, 90 and 115, with more 'or less sizable oblique parts at the baseand re-entering parts at the apex, depending on the case.

Finally, curve 37 gives the intersection of the for ward part of thereflector with the plane of symmetry. The drawing, as a whole,constitutes the diagram of the reflector and perfectly defines in spacethe elementary mirrors comprising the internal surface of said reflec-I01.

FIG. 8 represents a section of the reflector obtained according to thediagram of FIGS. 7a and 7b; it shows the source of light energyconsisting of a bulb 38 whose axis makes an angle of the order ofapproximately I5 with the vertical axis of the reflector, the back face39 of the projector with its lower rolled edge 40 and its upper edge 41folded back in the form of a hair-pin, the

forward face 42 with its lower rolled edge 43, its upper hollow back 44and its upper edge 45 folded back in the form of a hair-pin. The lightrays originating from the light source and striking the back face 39 arereflected in the direction of the work plane. Most light raysoriginating from the light source and striking the forward face 42, arereflected in the direction of the back face, which, mainly through thearea surrounding point 46, reflects them again in the direction of thework plane. A small number of light rays striking forward face 42,particularly those striking the area surrounding point 47, are reflectedtowards the back but outside the surface of the reflector, and aredesigned to create an environmental illumination. Similarly, certainrays striking the lateral areasof the reflector are used to create anenvironmental illumination around the actual work plane.

FIGS. 9a and 9b show the way illumination is distributed on the plane bya reflector of the type described in FIGS. 7a, 7b and 8.

Reflector 48, shown as a front view of FIG. 9a and as a plane view inFIG. 9b, located at a height H above a ground plane, concentrates aconsiderable quantity of light energy in a beam 49, bound by two endrays, one 50, marking an angle of the order of 30 to 40 with the groundplane, and the other 51, making an angle of the order of 15 to 20 withsaid ground plane. This light energy is distributed uniformly on a workplane 52 of almost rectangular shape. This work plane is surrounded, onthe one hand, by an area 53 located between said work plane and thereflector, also possibly containing the parts of the ground planelocated below the reflector and in which illumination is weaker than, orat most equal to that of the work plane 52, and on the other hand, bythree areas 54, 55 and 56 in which illumination rapidly decreasesstarting with the zone in the vicinity of area 52. Furthermore, an area57 is also created at the back of the projector and providesenvironmental illumination. For a height of the reflector above theground plane of the order of 30 cm, the left edge of work plane 52 isapproximately 35 cm away from the stand of the projector, its right edgeis approximately cm away from said stand and has a width of the order of45 cm, and inside this entire surface, the illumination is practicallyuniform.

SPECIFIC APPLICATION OF THE METHOD TO THE EMBODIMENT OF FIGS. 7a-9b Thefollowing discussion relates particularly to the specific embodiment ofFIGS. 7a-7b or 8, in the case of an incandescent transparent bulb, andwhen it is desired to illuminate a work plane on a writing table withthe particular light distribution which is illustrated on FIG. 9a.

The dimensions and respective light intensities for each of the portions52 to 57 in FIG. 9a are first calculated, starting from a considerationof the optimum physiological conditions which are desirable for theobserver, and from a consideration of the light flux generated by atransparent bulb located at normal height above the work plane. I

They are, in fact, the initial data from which the reflector shape willbe determined through application of the method.

The general shape of the reflector is next decided upon. As illustratedin FIGS. 7a-7b and 8, the projector has a pseudo-trapezoidal axialsection and two (one upper, one lower) circular baseapertures, thecenter (S, 1 FIG. 7a) of the upper aperture being offset (of about 20-30mm) with respect to the center of the lower aperture.

The lateral surface of the reflector comprises a rear face, two sidefaces and a forward face. The light rays originating from the bulb andstriking the back face are reflected on the work plane, and moreprecisely, they will illuminate portion 52, FIG. 9a. The light raysstriking the forward face will mainly illuminate the back face (in thearea surrounding point 46, FIG. 8) and be reflected back to the workplane (In other words, the forward face plays the part of a relay). Thelight rays striking the two side faces will illuminate portion 54 and55, FIG. 9a. By preference, in the general design of the particularreflector the back face is located as near as possible to the lightsource and adapted for illuminating the laterally offset area 52. Theforward face of the reflector is generally oriented such a way that thelight will not be substantially deflected thereon, thus coming backthrough the bulb and striking again the forward face of the reflectorbefore being finally reflected on area 56. For obtaining as smallreflection angles as possible on the said forward face, it has beengiven cross-sections having the form of circles centered at S (S alsobeing the center of the bulb). These circles are shown on FIG. 7a.

The illumination pattern is completed by light reflected from the twosides face of the reflectors, which provided crossed light beamsilluminating the areas 54 and 55. An upper conical face (44,'FIG. 8) isprovided, with an inclination with respect to the horizontal plane suchthat it will extend substantially in the direction of points S, thusavoiding any reflection of light thereon.

The direct illumination from the source covers the area 53 (FIG. 9a).

Once the general shape has been decided, each of the surface portions ofthe projector will be accurately calculated through application of themethod set forth above for the general case.

This method for the specific case, includes four steps:

A. The determination of a small number of points of the sections of theprojector in the median vertical plane containing S and in thehorizontal plane containing S and of the tangent planes to the reflectorat these points.

B. The detemiination of a large number of intermediate points of theprojector surface and of the tangent planes to the projector at thesepoints.

C. The determination of elementary fskew mirrors centered on thesevarious points.

D. The determination of the accurate. shape of templates which will beused in the effective manufacture of the reflector.

Step A is carried out as follows:

Very briefly, in the median verticalplane containing S, one firstlydetermines three points of the profile of the rear face of theprojector, namely: the point 0 which belongs to the horizontal linepassing through S and the two end points A and A (see FIG.

Point O is taken at about 8 mm from the bulb surface. Unmolding of theprojector can be easily effected when the minimum taper angle is atleast 1. Therefore, at lower point A, the inclination of the profilewith respect to the vertical should equal 1. Then, as the ray 8A shouldbe reflected on the right side of area 52, FIG. 9a, the reflected ray AR will be inclined by 16 with respect to the horizontal. (This iscalculated starting from the known position and dimensions of area 52).

It results that 8A should make an angle of about 14 with the horizontal.

Now, it is decided to take, for instance, A such that the line SA willmake an angle of about 25 with respect to the horizontal. As R should beon the left side of area 52, it may be shown that A R will be inclinedby 60 and it results that the mirror in A, should be inclined by 3730with respect to the vertical. Finally, the inclination of the profile in0 will be calculated for obtaining 0R making an angle of about 20 withrespect to the horizontal. Then, one may calculate that the mirror at 0should be inclined by 10. This enables one to roughly determine (bythree points and tangents) the profile A,OA which is tangent to thethree mirrors A 0 and A The same type of reasoning and calculationenables one to roughly determine (by a few points and the correspondingtangents) the section of the projector in the horizontal planecontainingS.

The first determination is a mixture of calculation and general commonsense considerations. However, it does not lead to something arbitraryand doesnot involve any trial and error.

The calculation of the inclinations of the tangent in A and O arecarried out through the application of the method disclosed above forthe general case. Among the common sense considerations are thefollowing:

a. choice of the position of point 0 b. choice of the angle OA S 0.choice of the minimum taper angle at A d. the decision that horizontalsections of the back' face of the reflector (only one of thesehalf-sections is shown at FIG. 7a) should reflect'light rays on all thearea of portion 52in FIG. 9a.

The practical reasons for these choices are reasonably imposed byconsiderations of convenience of manufacture and natural distribution ofthe flux of the bulb in space. I

Step B is carried out as follows:

Once the general envelope of the projector has thus been roughlydetermined, one takes a plurality of intermediate points P obtained asfollows: one will consider, on one hand 36 vertical planes containingthe axis of the projector and 16 conical surfaces having as their commonaxis the axis of the projector and apex angles increasing by 10 from oneconical surface to the following. Finally 16 X 36 576 solid angles arethus determined. Each of said solid angles delimits a pseudo-trapezoidalarea on the projector envelope and the central point of the said areawill give the approximate position of one point P.

Now, each of the said areas receives a certain light flux from thesource, and, as we know the photometric curves of the source, this fluxmay be exactly calculated, (without any supposition that the source ispinpoint light source).

After that, the method is carried out as illustrated by FIG. 9d.

For the few points P determined in step A, the corresponding points Rare exactly known and, also, the orientation of the tangent planes.Therefore, the images of the filament obtained by reflection on thesepoints may be exactly calculated, in size and light intensity.

For the other points P, the points R will be first positioned inregularly distributed intermediate portions and this will enable one tocalculate the tangent planes at the corresponding points P and theresulting images. If the resulting light distribution, as apparent fromFIG. 90, is not quite perfect, small corrections will be done throughslightly modifying the positions of some of the points R and the neworientations of the tangent planes will be calculated.

It is to be emphasized that this is not a trial-and-error matter, butrather a calculus of optimization. This calculus supposes that thereflector surface is made of a patchwork of plane small mirrors eachcentered at one of the points P and receiving a known light flux. Infact, in the final reflector, the elementary mirrors will not be plane.A small variation of the position of P only results in a very smalldisplacement of the image on the work plane, and a slightly imperfectlight distribution will not, anyway, be perceptible to the eye. When,however, it appears on the sketch that two many images concentrate insome regions and two few in others, it will be easy to select anotherposition for some points R and to again calculate the correspondingorientations of the small mirrors.

At the end of step B, one finally has, for instance, 576 points and thecorresponding tangent planes, which provides one with a very finedefinition of the reflector surface.

Step C is carried out as follows:

Then there are provided around each of the points P, an elementaryconcave skew" or warped mirror delimited by four arcs of circles, thesemirrors being determined in such a way that the tangent planes theretoat each point will exactly have the orientations calculated in step B.

The intersections of these elementary mirrors with the horizontal andvertical planes already defined are determined as illustrated in FIG. 9efor an horizontal intersection.

It is seen that the tangent at P intersects at m and n the lines sm andm inclined by 5 with respect to SP The tangent at m and n are thendetermined in such a way that the corresponding points R whichrespectively correspond to P and P and to P and P respectively. Now, thearc of circle which is tangent to the three tangents at m P and n willbe determined and only the portion m n' of it which will be retained.The same method will then be applied at P but now, a parallel to thetangent at n should be drawn at m This is why a small redan n m will beformed. If this redan is not small enough, one may divide each 5 angleby two and separately determine the skew mirror curvatures for the twohalf-mirrors thus defined.

The are of circles m; n and m';, n are obviously not centered at s,their respective centers are accurately calculated.

The same method is applied in the vertical planes.

Finally, one obtains a complete definition of the surface of theprojector through an assembly of skew mirrors each of which very closelyapproximates, as far as its reflection properties are concerned, theplane mirrors described in step B and yet enable one to obtain asmoother projector surface and, therefore, a smoother lightdistribution.

Step D is carried out as follows:

The mirrors defined in step C are not very easy to build because theyare delimited by conical surfaces above-defined. This is why thecalculations are made again for finally defining skew mirrors delimitedby equidistant horizontal planes, as illustrated in FIG. 7a. Thecurvatures of the new mirrors are already known in the vertical planes,which remain the same in step D. Calculation of the curvatures in thehorizontal planes is made by interpolation. Templates are then builtmanually with the exact shape determined for these new skew mirrors.These templates are used for manufacturing the mold or stamping die. Themolding process is conventional.

In fact, these mirrors are skew only in the rear and side faces of theprojector of the preferred embodiment. Their vertical sides areconnected to one another through steps or redans, as clearly apparentfrom FIG. 7a. Some of these redans are very small and practicallyunapparent. In fact, step C is carried out in such a way that the redansare as small as possible on the rear face, which leads to have a muchmore important redan 24, FIG. 7a) at the junction between the rear faceand each of the side faces.

SOME REFLECTIONS ON THE METHOD AS APPLIED TO THE PREFERRED EMBODIMENT Asexplained above in step B, the real photometric curves of the source aretaken into account when the images of the filament are calculated.

Only the points of the source such that a straight line joining them toP makes an angle below with the been determined by the above method, thecalculation of the image is within the reach of those skilled in theart.

The manner according to which the surface of the reflector is divided insmall areas is not arbitrary. Of course, one could take a or a 15division instead of the division described in step B. This is a questionof accurateness of the definition which is desired. A l0 division isfound sufficient in practice.

The method does not assume that each of the reflector areas is flat. Itmerely consists in calculating the orientation that the tangent plane tothe mirror should have at a finite number of points P for obtainingreflection at a corresponding number of points R. What is assumed isonly that the intermediate points P will provide reflection atintermediate points R which will be regularly distributed between thepoints R for which the calculations are effectively made. Thisassumption is perfectly correct, provided that the reflector surfacedoes not comprise important discontinuities between the points P forwhich the calculationsare made.

Snells law is applied in the calculation of the orientation of eachtangent plane. However, Snells law consists in effecting the calculationon one plane of reference, and not in an X Y Z axis-system. The methodof calculation which is disclosed herein is, as far as is known, novel.This is an application of descriptive geometry which has not been madebefore.

Any point R can be associated, a priori, with a given point P. However,once the image of the source which is obtained on a plane mirror locatedat P and oriented in such a way that the light is focused around a givenpoint R has been determined in size and intensity, and once suchdetermination has been made for a plurality of couples of given points Pand R, it will but remain to properly modify the positions of the pointsR until corresponding images (which will not, in practice, vary inintensity and size) form a continuous pattern on the area to beilluminated. For each modification of the position of a point R, thecorresponding modification which should be effected on the orientationof the plane mirror at P will be easily calculated. The initial choiceof points P and R is not arbitrary, but a mere matter of optimization.The following modification of the position of points R are butminorcorrections. The

whole process is fully mastered through calculation and practically notrial-and-error job is involved therein.

All of the reflectors obtained through application of the method willcomprise an assembly of elementary mirrors each having a skew surface,(in French: surface gauche, which does not only mean curved: a sphere ora cylinder have no skew surfaces) delimited by four arcs of a circle,said mirrors having their vertical sides connected together throughredans.

Apart from these skew mirrors, all the reflectors obtained through themethod will comprise at least one light relay portion (as the front 42portion of the reflector in FIG. 8) adapted for reflecting the lightfrom the source on to the skew mirrors.

Cooperation of skew mirrors portions which directly reflect the light onthe area to be illuminated with relay portions are another feature ofthe invention.

A purely trial-and-error designing would consist in modifying the shapeof the reflector until a certain distribution of light is obtained: thismeans measuring the geometrical shapes would be used in atrial-and-error method.

Portion 44 of the top surface does not play any part in the lightdistribution and is but an unavoidable linking surface. Portion 44 hasbeen shaped so as substantially to avoid any reflection from lightthereon, and thus, does not disturb the light distribution as determinedby the other portions of the reflector.

The orientations of the tangent planes in a vertical section vary verylittle from the top to the bottom of the reflector. However, theorientations of the tangent planes in an horizontal section aresubjected to a comparatively large variation for instance from mirror 20(in FIG. 7a) to the mirror adjoining mirror 24. This results from thedetermination of the general envelope of the reflector, in accordancewith step A of the method. This determination also provides that themirrors of the side portions of the reflector should have a givenorientation.

It is clear from FIG. 7a, that this implies the presence of a largeredan 24, if one desires to avoid getting out of the generally circularhorizontal section. Finally, the redans are a practical way of linkingtogether a plurality of mirrors having predeterminal orientations andgenerally located within a predetermined roughly cylindrical envelope.They do not perform a positive function in the light distribution.

The socket may be mounted inside the top of the reflector. This willavoid projecting any shade on the ceiling. However, this should not atall be considered as a necessary feature of the invention and the bulbcould be positioned in other ways, forinstance, as depicted.

The flaring at 28-35, FIG. 7b results from the specific method ofmanufacture which has been used and is not part of the invention.

Various shapes and types of incandescent light bulbs are manufacturedthroughout the world. This will not require the use of different typesof reflectors. In fact, what essentially matters for determining theshape of the reflector is the filament position (not the filament orbulb shape).

This position may be adjusted through the use of different types ofsockets.

THE REMAINING ILLUSTRATED EMBODIMENTS FIG. 10 shows another example ofthe construction of a reflector according to the invention usingpreferably an opalescent or frosted bulb. Inside contour 58 which boundsthe external surface of the reflector, may be seen reflecting surfaces59, 60, 61, 62, 63, 64, 65 and 66 separated by bends 67, 68, 69, 70, 71and 72 distributed over the lateral surface of the reflector.Furthermore, in order to recover the light energy emitted by the bulb inthe direction of the upper wall of the projector, additional reflectingsurfaces were formed on this wall; those numbered 73, 74, 75, 76 and 77separated by bends 78, 79 and 80 send back the light energy which theyreceive, towards the work plane, and those numbered 81 and 82 send backthe energy which they receive, upwards, through openings made in theupper back of the projector, thus creating an environment.

It is also possible to place mirrors such as 83 below the'bulb whichprevent the light emitted downwards by the bulb from creating an area ofintense illumination at the stand of the reflector which is generallyundesirable. The said mirrors send back said light towards the workplane through opening 84. Finally, it is also possible to place, belowthe bulb, mirrors such as 85 which send back the light directly towardsmirrors such as 62 or 75 from which it is directed towards the workplane.

FIGS. 11a and 11b show a reflector 86 constructed according to anotherembodimentof the invention and partially enveloping a brightincandescent bulb 87', the entire assembly being placed inside alampshade 88 which may or may not be translucent, giving mainly adecorative effect obtained by masking the bulb-reflector assembly. Saidreflector, for example, may be constructed by pressing a polished andanodized aluminum plate. A very strong useful illumination is thusobtained in a lateral direction with respect to that which might beobtained using a lamp not provided with a reflector.

FIGS. 12a and 12b show another design of a projector 89 partiallysurrounding a light source which can be advantageously used for lightingshop windows.

FIG. 13 shows a cut-away section of a decorative glassware arrangementobtained by molding, in which the lower part 90 has been molded on acore calculated so as to have the same characteristics as the internalsurface of the projector shown in FIGS. 7a-7b, said lower part 90 beingcoated internally with a deposit of glossy material applied undervacuum, thus giving to this part the character of a reflector while theupper part 91, not coated with glossy material, remains translucent, andcontributes to an environmental illumination. These glasswarearrangements will be used in a valuable manner as a bedside or work lampor still as wall fittings.

FIGS. 14a and 14b are similar to FIG. 3, but relate to a fluorescenttube. These figures show a solid angle of apex P containing all the raysoriginating from fluorescent tube 92, ending up at P and making an anglewiththe perpendicular to said fluorescent tube, which is smaller than,or at most equal to 60. As shown, these rays are those which send thestrongest contribution in radiating energy to point P. The total sum ofrays reflected by point P in the direction of the work plane to beilluminated and corresponding to rays providing a strong contribution inenergy as determined above, is contained in a cone of apex P which has aright section in the form of a very elongated oval, whose centralstrongly illuminated zone may be perfectly defined as far as value, formand direction are concerned. The various reflecting surfaces comprisingthe reflector may therefore, in accordance with the method disclosedhereinabove, be determined so as to solve a particular illuminationproblem such as the illu mination of a desk, shop, classroom, etc.

FIGS. a and 15b show a reflector 93, constructed according to the methoddisclosed hereinabove and providing for the distribution of light energyproduced by a fluorescent tube 94 on a defined work surface. FIGS. 16a,16b and 160 show another embodiment of a reflector associated with afluorescent tube. The internal surface 95 of this reflector comprisessets of elementary reflecting surfaces forming a checker-work.

orientation of these elementary reflecting surfaces makes it possible togive a very inclined orientation to'the image of the source on the workplane with respect to the axis of the fluorescent tube, which can evenextend to a position perpendicular to said axis. This arrangement isparticularly valuable, for it makes it possible to illuminate a roomwith devices located on the sides and therefore outside the visual fieldof the users located in the central part of said room.

The devices according to FIGS. 15a-15b and 16a-16b-l6c may be provided,at the stand of the tube, with opaque plates whose dimensions aresuitable for masking the tube from direct view. These devices may, inaddition, if necessary, be closed by Plates made of spa e tmateria sSuch projectors may be constructed by those skilled in the art by anyappropriate means, in particular, by pressing or cambering of metalplates ultimately polished by any appropriate means or still further bymolding of metals, glass or plastic materials which can eventually bepolished by any appropriate means, or still further by forging,spinning, milling of a metal block or other.

What is claimed is:

1. A reflector for an illuminating device which has a light source forreflecting light, emanating from the light source, upon a work surfaceto illuminate the work surface according to a pattern, said reflectorcomprising:

a plurality of elementary reflecting surfaces each having an upper edge,a lower edge and two opposite side edges, said reflecting surfaces beingdisposed adjacent one another in at least one group having substantiallycontinuous transitions between edges of vertically adjacent reflectingsurfaces and having discontinuous, stepped transitions between edges oflaterally adjacent reflecting surfaces;

each of said elementary reflecting surfaces comprising a skew concavemirror, each of the four said edges thereof being an arc of a circle,each of the four arcs being of different curvature;

the skew concave mirrors in said one group being individually orientedto collectively reflect light from said light source to an area of thework surface which is offset from being aligned with he portion, twolaterally opposite side portions and a front portion and having a topwall surmounting said sidewall;

means defining an upper circular opening through said top wall and meansdefining a lower circular opening of said structure at and bounded bythe lower periphery of said sidewall, said upper circular opening havinga center which is substantially offset from the center of said lowercircular opening toward said rear portion of said sidewall;

said structure being symmetrical about an axially extending diametralplane extending through said centers and bisecting said front portionand said rear portion;

said at least one group of elementary reflecting surfaces comprisingsaid skew, concave mirrors being disposed upon one of said sidewall sideportions;

said at least one group of elementary reflecting surfaces furthercomprising a second group of elementary reflecting surfaces comprisingskew, concave mirrors each having an upper edge, a lower edge and twoopposite side edges, said reflecting surfaces being disposed adjacentone another in at least one group having substantially continuoustransitions between edges of vertically adjacent reflecting surfaces andhaving discontinuous, stepped transitions between edges of laterallyadjacent reflecting surfaces; each of the four edges of each skew,concave mirror of said second group being an arc of a circle, each arcof the four arcs being of different curvature;

said second group of elementary reflecting surfaces comprising skew,concave mirrors being disposed on the other of said sidewall sideportions;

the front portion of said sidewall having substantially circular-arccross-sections in planes perpendicular to the longitudinal axis of saidupper circular openmg;

the rear portion of said sidewall having means defining a plurality ofstepped reflecting surface portions thereon;

the rear portion being disposed to reflect light incident thereon fromsaid light source to an area of said work surface below said reflectoroffset in the direction of the front portion of said structure sidewall;and

the front portion being arranged for reflecting most of the lightincident thereupon toward the rear portion of said sidewall.

3. The reflector of claim 2 wherein said top surface, adjacent saidupper circular opening and adjacent said front portion of said sidewallis generally conically curved in a sector arranged to avoid incidence oflight thereon from said light source.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION' Patent No. 3,TOO, 882 Dated October 2 4, 1972 Inventor(s) Jean PlanChOn It iscertified that error appears in the above-identified patent and thatsaid Letters Patent are hereby corrected as shown below:

Add to the heading:

Foreign Application Priority Data January 12, 1967 France 90,783

Signed and sealed this 13th day of March 1973.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT 3OTTS CHALK. Attesting Officer Commlsslonerof Patents F ORM PO-OSO (IO-69) USCOMM-DC 6Q37b-P69 n us. GOVERNMENTFRINHNG O'IICI nu o-asa-ua

1. A reflector for an illuminating device which has a light source forreflecting light, emanating from the light source, upon a work surfaceto illuminate the work surface according to a pattern, said reflectorcomprising: a plurality of elementary reflecting surfaces each having anupper edge, a lower edge and two opposite side edges, said reflectingsurfaces being disposed adjacent one another in at least one grouphaving substantially continuous transitions between edges of verticallyadjacent reflecting surfaces and having discontinuous, steppedtransitions between edges of laterally adjacent reflecting surfaces;each of said elementary reflecting surfaces comprising a skew concavemirror, each of the four said edges thereof being an arc of a circle,each of the four arcs being of different curvature; the skew concavemirrors in said one group being individually oriented to collectivelyreflect light from said light source to an area of the work surfacewhich is offset from being aligned with he light source; the pluralityof elementary reflecting surfaces further including at least oneadditional group thereof having substantially continuous transitionsbetween edges of vertically and laterally adjacent reflecting surfaces;and the concave mirrors in said one additional group being individuallyoriented to collectively reflect light from said light source onto saidat least one group comprising said skew, concave mirrors.
 2. Thereflector of claim 1 comprising: a generally inverted bowl-shapedstructure having a generally cylindrical sidewall divided into a rearportion, two laterally opposite side portions and a front portion andhaving a top wall surmounting said sidewall; means defining an uppercircular opening through said top wall and means defining a lowercircular opening of said structure at and bounded by the lower peripheryof said sidewall, said upper circular opening having a center which issubstantially offset from the center of said lower circular openingtoward said rear portion of said sidewall; said structure beingsymmetrical about an axially extending diametral plane extending throughsaid centers and bisecting said front portion and said rear portion;said at least one group of elementary reflecting surfaces comprisingsaid skew, concave mirrors being disposed upon one of said sidewall sideportions; said at least one group of elementary reflecting surfacesfurther comprising a second group of elementary reflecting surfacescomprising skew, concave mirrors each having an upper edge, a lower edgeand two opposite side edges, said reflecting surfaces being disposedadjacent one another in at least one group having substantiallycontinuous transitions between edges of vertically adjacent reflectingsurfaces and having discontinuous, stepped transitions between edges oflaterally adjacent reflecting surfaces; each of the four edges of eachskew, concave mirror of said second group being an arc of a circle, eacharc of the four arcs being of different curvature; said second group ofelementary reflecting surfaces comprising skew, concave mirrors beingdisposed on the other of said sidewall side portions; the front portionof said sidewall having substantially circular-arc cross-sections inplanes perpendicular to the longitudinal axis of said upper circularopening; the rear portion of said sidewall having means defining aplurality of stepped reflecting surface portions thereon; the rearportion being disposed to reflect light incident thereon from said lightsource to an area of said work surface below said reflector offset inthe direction of the front portion of said structure sidewall; and thefront portion being arranged for reflecting most of the light incidentthereupon toward the rear portion of said sidewall.
 3. The reflector ofclaim 2 wherein said top surface, adjacent said upper circular openingand adjacent said front portion of said sidewall is generally conicallycurved in a sector arranged to avoid incidence of light thereon fromsaid light source.